MI5 has launched two urgent inquiries into how it missed the danger posed by the Manchester bomber, Salman Abedi, amid claims his interest in being a potential terrorist killer was repeatedly reported to the authorities.

Britain’s domestic security service started one review last week, which will aim to quickly identify any glaring errors, while the other will be more in depth, the Guardian has learned.

On Sunday, the home secretary, Amber Rudd, refused to comment on whether opportunities were missed to spot the murderous intent of the 22-year-old before his deadly attack, as national security became the major issue in the general election campaign.

The reviews come with security officials warning that the threat from Islamist terrorism keeps rising and is at an “unprecedented scale”, with other attack plots feared.

A 23-year-old man was arrested in the early hours of Monday in Shoreham-by-Sea, Sussex, on “suspicion of offences contrary to the terrorism act”, Greater Manchester police said, bringing to 14 the number in custody related to the Manchester attack inquiry.

The fallout from the tragedy has triggered an intense war of words across the political spectrum, with Rudd claiming that there would be a greater risk of another atrocity if Jeremy Corbyn became prime minister.

As she accused the Labour leader of voting against anti-terror measures, with “no evidence he will keep people safe”, her Labour counterpart, Diane Abbott, hit back by claiming that government cuts, including to the police and border force, have “consequences”. Diane Abbott: ‘My hairstyle has changed and so have my views’

“Citizens have a right to expect that the government sets their safety and protection as their number one priority and provides the resources to achieve that. It is no exaggeration to say that this government has failed in that elementary duty,” the shadow home secretary told the Guardian.

Investigators believe Abedi, whose parents come from Libya, may have received terrorist training in the country, where some areas are believed to be a safe haven for jihadis. He returned to the UK from Libya just days before exploding a homemade bomb packed with metal bolts and screws, carried in a rucksack, murdering 22 people after the Ariana Grande concert at Manchester Arena on Monday 22 May.

Teachers and religious figures in Manchester who knew Abedi raised concerns about his extremist views on multiple occasions and over several years.

MI5 is believed to have conducted a quick review of the intelligence held about Abedi last week, but the inquiry was limited as the agency’s focus and resources were poured into the manhunt and recovering the materials linked to the bomb.

The second review will be more detailed and look at the decision-making around Abedi before his attack. A source said the key question, given what is now evident about the danger Abedi posed, would be: “Would different decisions be made?”

The longer review will look at the processes and systems used to assess suspects and what was known about any of the other main conspirators. The system of assessing and managing risk used by MI5 is coming under immense strain, given the service’s unrelenting and rising workload.

Abedi had been examined by security service case officers in the past, but by last Monday was one of a pool of 20,000 one-time Islamist jihadi suspects. He was not one of the 3,000 people under active investigation.

MI5 says it has to prioritise which suspects it devotes its limited investigative resources to, to whom are deemed most dangerous. Rudd, speaking on the BBC1’s Andrew Marr Show on Sunday, said she did not want to “rush to conclusions” about intelligence failures.

But she added: “We won’t shy away from looking at what we can do to keep people safe. We are in constant discussion with the security services and the police to make sure they have the right tools they need.”

Rudd warned that further members of Abedi’s network could still be at large. Speaking shortly before fresh raids were launched in Moss Side, Manchester, on Sunday afternoon, the home secretary warned: “We can’t be entirely sure that [the Manchester operation] is closed.” Amber Rudd: Manchester terror network members ‘may still be at large’

A 25-year-old man was arrested on Sunday in the Old Trafford area of Manchester on suspicion of offences contrary to the Terrorism Act, bringing the total number of arrests linked to the attack to 14. A dozen of those remain in custody for questioning and two have been released without charge. Charges are expected against some.

In Brussels on Thursday, Theresa May confronted Donald Trump at a Nato meeting over the leak of detailed intelligence about the attack, which was shared across the Atlantic and published by the New York Times.

On Sunday, the president responded on social media, saying that May had been “very angry” about the leak.

May also addressed the issue in the context of the general election on the second leg of her trip to the G7 summit in Sicily, claiming Corbyn had blamed the UK for the terror attack. Her intervention came after the Labour leader said the war on terror was not working, in a speech that angered his critics because it came just days after the Manchester attack.

Meanwhile, Max Hill QC, the government’s independent reviewer of terrorism legislation, wrote in the Telegraph that more resources, not new laws, were needed to deal with the terror threat.

Intelligence officials have come under fire after past atrocities. Both of the killers of fusilier Lee Rigby, who was murdered in London in 2013, had been subjects of interest for their extremist views before the attack but had not been under active surveillance. MI5 also faced claims they missed a chance to stop the ringleader of the 7 July 2005 bombing of London, Mohammad Sidique Khan.

Parliament’s intelligence and security committee may want to investigate the Manchester bombing, and inquests can be turned into broader inquiries if coroners agree. Privately, at least one cabinet minister has previously questioned MI5’s overall competence and the security service accepts it has hard questions to answer.

MI5 is getting more money and hiring more staff but the increase in its capacity – it now employs about 4,000 staff – will still take some time to be felt.

The level of terrorist activity directed at the UK is at an “unprecedented scale”, sources say, and is believed by counter-terrorism officials to have kept growing since last year.

In October 2015, the MI5 director general, Andrew Parker, gave a rare speech warning: “We have seen greater ambition for mass-casualty attacks. It may not yet have reached the high-water mark, and despite the successes we have had, we can never be confident of stopping everything.”

It emerged for the first time on Sunday that suspected Islamic terrorists are being prevented from returning to the UK after fighting abroad under new temporary exclusion orders.

Rudd admitted the authorities did not know how many Britons had returned from fighting with Islamic State or other extremist groups and refused to say how many times exclusion orders had been used. “We have started to use them,” she said.

The Liberal Democrats also waded into the debate over counter-terrorism policy, with Nick Clegg accusing May of creating a “direct threat to our national security” through her approach to Brexit.

The former deputy prime minister said the UK police and security services used an EU-wide database on organised criminal and terrorist suspects more than half a billion times last year – equivalent to 16 times a second.

“Theresa May’s extreme approach to Brexit will have the direct consequence of severing our ties to a fantastically useful weapon in our armoury against terrorism,” he said. “By refusing to accept a role for the European court of justice in policing this European-wide database, she has ruled out our future participation it.”

A Conservative spokesman said: “We’ve made clear that under Theresa May security cooperation will be an important priority in the negotiations, in the interests of both sides.

“This is a matter for the negotiations but what is absolutely certain is that a good Brexit deal can only be achieved under the leadership of Theresa May and her Conservative team. A vote for the Lib Dems just puts Jeremy Corbyn one step closer to Downing Street, undermining our national security and making a mess of the Brexit negotiations.”